The harmonic Rayleigh–Ritz extraction has been introduced in the context of eigenvalue problems (see, e.g., [1]}, [2]}, [3]}, [4]}) to extract promising approximate (interior) eigenpairs from a subspace. Consider the eigenproblem \(A\mathbf {x}= \lambda \mathbf {x}\)  for a given square \(A\) . Although \(A\)  does not necessarily need to be symmetric or real for the harmonic extraction method, in our optimization context we are interested in real symmetric matrices SPD matrices \(A\) .
